Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States. In Australia, only 1.5% of the population has blood type AB. Suppose a random sample of 50 U.S. residents and 40 Australians is obtained. Consider the random variables described below:X: the number of US residents (out of 50) with blood type AB.Y: the number of Australians (out of 40) with blood type AB.Z: the total number of individuals (out of 90) with blood type AB.Which of the following is true about the random variables X, Y, and Z? Check all that apply. X is a binomial random variable with n = 50 and p = 0.04 Y is a binomial random variable with n = 40 and p = 0.015 Z is a binomial random variable with n = 90 and p = 0.055Question 2Select one answer.10 pointsIn the following random experiment, decide whether the random variable X is binomial or not:Approximately 1 in 10 people are left-handed. Let X be the number of people that are left-handed out of a random sample of 200 individuals. Although the individuals are sampled without replacement, it is assumed that we are sampling from such a vast population that the selections are virtually independent. Binomial Not binomialQuestion 3Select one answer.10 pointsBlood type AB is the rarest blood type, occurring in only 4% of the population in the United States. In Australia, only 1.5% of the population has blood type AB. Suppose a random sample of 50 U.S. residents and 40 Australians is obtained. Consider the random variables described below:X: the number of U.S. residents with blood type ABY: the number of Australians with blood type ABWhat is the probability that exactly 2 of the U.S. residents have blood type AB? (Note: Some answers are rounded) 0.2762 0.04 0.1334 0.0988 0.2646Question 4Type numbers in the boxes.Part 1: 10 pointsPart 2: 10 points20 pointsIn Texas, 30% of parolees from prison return to prison within 3 years. Suppose 15 prisoners are released from a Texas prison on parole. Assume that whether or not one prisoner returns to prison is independent of whether any of the others return to prison. Let the random variable X be the number of parolees out of 15 that return to prison within 3 years. What are the values of the parameters for the binomial random variable X?n = p =
Question
Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States. In Australia, only 1.5% of the population has blood type AB. Suppose a random sample of 50 U.S. residents and 40 Australians is obtained. Consider the random variables described below:X: the number of US residents (out of 50) with blood type AB.Y: the number of Australians (out of 40) with blood type AB.Z: the total number of individuals (out of 90) with blood type AB.Which of the following is true about the random variables X, Y, and Z? Check all that apply. X is a binomial random variable with n = 50 and p = 0.04 Y is a binomial random variable with n = 40 and p = 0.015 Z is a binomial random variable with n = 90 and p = 0.055Question 2Select one answer.10 pointsIn the following random experiment, decide whether the random variable X is binomial or not:Approximately 1 in 10 people are left-handed. Let X be the number of people that are left-handed out of a random sample of 200 individuals. Although the individuals are sampled without replacement, it is assumed that we are sampling from such a vast population that the selections are virtually independent. Binomial Not binomialQuestion 3Select one answer.10 pointsBlood type AB is the rarest blood type, occurring in only 4% of the population in the United States. In Australia, only 1.5% of the population has blood type AB. Suppose a random sample of 50 U.S. residents and 40 Australians is obtained. Consider the random variables described below:X: the number of U.S. residents with blood type ABY: the number of Australians with blood type ABWhat is the probability that exactly 2 of the U.S. residents have blood type AB? (Note: Some answers are rounded) 0.2762 0.04 0.1334 0.0988 0.2646Question 4Type numbers in the boxes.Part 1: 10 pointsPart 2: 10 points20 pointsIn Texas, 30% of parolees from prison return to prison within 3 years. Suppose 15 prisoners are released from a Texas prison on parole. Assume that whether or not one prisoner returns to prison is independent of whether any of the others return to prison. Let the random variable X be the number of parolees out of 15 that return to prison within 3 years. What are the values of the parameters for the binomial random variable X?n = p =
Solution
Question 1: X is a binomial random variable with n = 50 and p = 0.04. This is true because the sample size is fixed (50 US residents), the probability of success (having blood type AB) is constant (0.04), and the trials are independent (one person having blood type AB does not affect another person's blood type).
Y is a binomial random variable with n = 40 and p = 0.015. This is true for the same reasons as X, but with different values for n and p (40 Australians and a 0.015 probability of having blood type AB).
Z is not a binomial random variable with n = 90 and p = 0.055. This is because the probability of success is not constant. The probability of a person having blood type AB depends on whether they are from the US or Australia.
Question 2: The random variable X is binomial. This is because the sample size is fixed (200 individuals), the probability of success (being left-handed) is constant (0.1), and the trials are independent (one person being left-handed does not affect another person's handedness).
Question 3: The probability that exactly 2 of the U.S. residents have blood type AB can be calculated using the binomial probability formula: P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)), where n is the number of trials, k is the number of successes, p is the probability of success, and C(n, k) is the binomial coefficient. Plugging in the given values, we get P(X=2) = C(50, 2) * (0.04^2) * ((1-0.04)^(50-2)). This calculation will give the correct answer.
Question 4: The values of the parameters for the binomial random variable X are n = 15 and p = 0.3. This is because the sample size is fixed (15 parolees), the probability of success (returning to prison within 3 years) is constant (0.3), and the trials are independent (whether or not one parolee returns to prison does not affect whether any of the others return to prison).
Similar Questions
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